Search for Electroweakinos in R-Parity Violating SUSY with Long-Lived Particles at HL-LHC

We investigate the R-parity violating (RPV) supersymmetric (SUSY) model at the High-Luminosity Large Hadron Collider (HL-LHC) in the context of compact muon solenoid (CMS) experiment assuming a total integrated luminosity of $\mathcal{L}=3000~\text{fb}^{-1}$ at $\sqrt{s}=$ 14 TeV. We focus on the pair production of electroweakinos, specifically, $\chi_2^0$ and $\chi_1^{\pm}$ in wino and higgsino states in a particular scenario where $\chi_2^0$ and $\chi_1^{\pm}$ decay into a Higgs boson and W boson, respectively, along the long-lived lightest supersymmetric particle (LSP), $\chi_1^0$, which decays to three quarks via $\lambda^{''}$ RPV couplings leading to the prompt as well as displaced signatures in the final state. To select events at the level-1 (L1) trigger system, we employ dedicated and standard triggers followed by an offline analysis integrating information from the tracker, electromagnetic calorimeter (ECAL) and minimum ionising particle (MIP) timing detector (MTD). We observe that wino-like $\chi_2^0/\chi_1^{\pm}$ with a mass of 1900 GeV and $\chi_1^0$ with a mass greater than 800 GeV can be probed across a decay length ranging from 1 cm to 200 cm. In the case of higgsino-like pair production of $\chi_2^0/\chi_1^{\pm}$, we can probe $\chi_2^0/\chi_1^{\pm}$ with a mass of 1600 GeV, and $\chi_1^0$ with a mass greater than 700 GeV, across a decay length range of 1 cm to 200 cm.